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On the distributional fractional derivative: from unidimensional to multidimensional
  • ABDERACHID SAADI
ABDERACHID SAADI
Universite Mohamed Boudiaf M'sila

Corresponding Author:[email protected]

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Abstract

In this paper, we use the generalized notions of Riemann-Liouville (fractional calculus with respect to a regular function σ) to extend the definitions of fractional integration and derivative from the functional sense to the distributional sense. First, we give some properties of fractional integral and derivative for the functions infinitely differentiable with compact support. Then, we define the weak derivative, as well as the integral and derivative of a distribution with compact support, the integral and derivative of a distribution using the convolution product. Then, we generalize those concepts from the unidimensional to the multidimensional case. Finally, we propose the definitions of some usual differential operators.
09 Aug 2023Submitted to Mathematical Methods in the Applied Sciences
09 Aug 2023Assigned to Editor
09 Aug 2023Submission Checks Completed
16 Aug 2023Review(s) Completed, Editorial Evaluation Pending
22 Aug 2023Reviewer(s) Assigned